Question

If the lines 2x – ky + 5 = 0, 3x + 4y = 7, and 3kx - 5y + 8 = 0 are
concurrent, then find the value of k.​

Answer 1

Answer:

The line L: 3x-4y+5=0 is parallel to 3x+ky+10=0. How do I find the value of K?

3 x -4 y +5 = 0 [covert this equation in the form y=m x +c]

-4 y = -3 x -5 [multiply both sides by - sign]

4 y = 3 x +5

y = 3/4*x + 5/4

Slope of this line is 3/4.(m)

Equation of the parallel line 3 x +k y + 10 = 0

k y = -3 x -10 [change in the form of y = m x + c]

y = - 3/k -10/k

Slope of this line is -3/k (m)

Since two lines are parallel , slopes (m) must be equal

3/4 = - 3/k

3/4 = 3/-k

k = -4